Profitability Question and Example

Quote from riskfreetrading:

1. Do not trade stocks, trade indices.
2. Given you are a statistician, you understand how to evaluate probs, and test hypothesis.
3. What do you think are the chances for someone to determine the top price at a precise time using one minute closing price? (There are 360 minutes in a trading day (cash session).
4. Same question as 3. but now do it for 3 days in four consecutive days.

Why am I asking? Read my latest threads in which I posed (it is not the first time) the question. People who hanged in there are clueless to the nature of the question.

Also, I am also the man who nailed 3. and 4. last week.
Some backholders did not comprehend the possible significance of what I did, and insulted me for doing it even AFTER the market showed I am right.

What are my chances from a statistical sense to answer 3. and 4. correctly?
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I love it. Good question. By the way, I'm searching for the thread now. Which one is it? Thanks.

If I understand you correctly, you're asking what is the probability of predicting the high in a given day at a given minute out of 360 trading minutes, and given only the closing price of the prior day? That would take some thought, and couldn't possibly take into account an unstated method of course, but for a random comparison (that is, no method), that probability has to be pretty slim.

Good job. All right, now I'm dying to see this thread :)
 
Quote from zerfetzen:

I love it. Good question. By the way, I'm searching for the thread now. Which one is it? Thanks.

If I understand you correctly, you're asking what is the probability of predicting the high in a given day at a given minute out of 360 trading minutes, and given only the closing price of the prior day? That would take some thought, and couldn't possibly take into account an unstated method of course, but for a random comparison (that is, no method), that probability has to be pretty slim.

Good job. All right, now I'm dying to see this thread :)
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http://www.elitetrader.com/vb/showt...37&perpage=6&highlight=935am ndx&pagenumber=1

http://www.elitetrader.com/vb/showthread.php?s=&threadid=126528&perpage=6&pagenumber=11

http://www.elitetrader.com/vb/showthread.php?s=&threadid=126528&perpage=6&pagenumber=13
 
here another link for you:

http://www.elitetrader.com/vb/showthread.php?s=&threadid=126055&highlight=1111AM

Also your understanding is correct (or close) to reach the main point. I would also add to your understand of the question the idea of measuring the top from the time of the call until 390 minutes later. That will eliminate the need of the previous day close.

I advise you not to consider rule out this business, as you have a main weapon (you understand probabilities). You will notice that in my threads, I asked those questions specifically. I do not think that the majority in there even understood the significance of my question (but you got it immediately). Those people state that they are veterans and successful traders. I have no reason to doubt that, but I would say if you understood in one minute what the veterans did not seem to understand (some of them seem to even have written books and teach), then I think you have a great future.

You are about to be handed the keys to your ATM.
 
I'll take a crack at the probability, kind of a cheap crack and suggest that without prior information the probability of correctly estimating a high in a given day at a given minute is asymptotic to infinity as the granularity of the units approaches infinity...that is also saying that I don't know how granular the units go, myself.

If you buy and sell, or short as the case may be, I'm guessing everything is truncated or rounded to two decimal places, complicit with our currency.

Of course, in a Bayesian sense, the probability of a correct estimate will divulge from infinity as more information is accounted for. For example, I don't know the stock index (I'm assuming), and it could normally trade in the $5 range or $2,000,000 range, for all I know.

I think like a Bayesian, so with no prior information, I'm suggesting approximately infinity. But knowing how information can radically change that answer, I'll cheese out and say that the credible interval is negative infinity to infinity. How's that for starters :p
 
You intuition is in the right direction, and you already established the first result:

1. If you increase the lenghth of a bar in terms of time, then your probability should be higher.

A corrollary of the above is that if you have two services that provide timing information, and have the same win to loss ratio, you would then know that the one with a short time frame is more skillful that the other one.

Do you agree?

Let us put the case of infinity on the side (at least for the moment). Let us assume that the discretization of time is at least an interval delta (for instance 1 minute).

Let me give some assumptions to work with.

Let us assume that price changes at a times (t) as measured relative to previous bar (t-1), prices changes are denoted P(t), for the same bar size (which is the length of discretization interval) are independent and identically distributed (but may not have necessarily the same variance).

Could you now say something given the above assumptions?

PS: I have thought to give this question for the whole forum and call on those who were putting trash in the threads referenced above, and call on them to see if they have teeth, and if they do, who will not lose his teeth in the question . I already called on one guy (XFLAT...), and I found out that he was teethless, but he continued to speak, you know how it comes across :)

I may send you some hints in a PM. what do you think?

Also work with this ETF stock: QQQQ
 
I agree that more granular units of time usually give more to work with. I'm enjoying daily data, and if successful with it and trading in general to my satisfaction, look forward to subscribing to intraday data in the future.

In a sequence of p(t) to p(t-n), I cannot agree with the iid (independent and identically distributed) assumption, though. Take a traditional statistical forecasting model (any one of several) for example, and the presence of autocorrelation should indicate that p(t) is not independent of p(t-n) in a proper model based on AR-n.

Or similarly for my pattern recognition approach. Every stock I've looked at so far, including QQQQ just now, has not indicated support for the iid assumption.

But if iid does hold, it certainly makes things simpler.

Please PM me, I'm always up for modeling. Always. Cheers.

PS
My model indicates that the Low for QQQQ should decrease (est. prob=0.685621) with at least 2:1 odds. How far will it decrease? I don't have any confidence around that yet, but I'd say Monday's most likely Low for QQQQ is $47.63 according to my model. But of course, if QQQQ doesn't decrease, it is a probablistic estimate, but I could do this a string of times with similar criteria, and it should be right 68-70% of the time, so I'm thrilled. The other QQQQ series I have (Open, High, etc.), I got weak probability estimates, so I'm overlooking those series at the moment.
 
Cool it there, most people here are not statistician. Even though I had one class in stat and a whole load of advanced math I don't consider it closely related to trading. Stats are good but approximation is not for me. I like the real fundamentals along with the proven technical skill set of analysis, as they are more so proven. I can definitely say that your method is probable but I can't say that for everyone else because the subject seems vague and to the normal eye it's not a very popular. So don't hold it as absolute because it will never be accepted as normal strategy for trading...

sg20
 
I'd never ram something down other people's throats; to each his own. But I do think this is an appropriate thread to discuss statistics if anyone's interested.
 
Quote from zerfetzen:

I agree that more granular units of time usually give more to work with. I'm enjoying daily data, and if successful with it and trading in general to my satisfaction, look forward to subscribing to intraday data in the future.

In a sequence of p(t) to p(t-n), I cannot agree with the iid (independent and identically distributed) assumption, though. Take a traditional statistical forecasting model (any one of several) for example, and the presence of autocorrelation should indicate that p(t) is not independent of p(t-n) in a proper model based on AR-n.

Or similarly for my pattern recognition approach. Every stock I've looked at so far, including QQQQ just now, has not indicated support for the iid assumption.

But if iid does hold, it certainly makes things simpler.

Please PM me, I'm always up for modeling. Always. Cheers.

PS
My model indicates that the Low for QQQQ should decrease (est. prob=0.685621) with at least 2:1 odds. How far will it decrease? I don't have any confidence around that yet, but I'd say Monday's most likely Low for QQQQ is $47.63 according to my model. But of course, if QQQQ doesn't decrease, it is a probablistic estimate, but I could do this a string of times with similar criteria, and it should be right 68-70% of the time, so I'm thrilled. The other QQQQ series I have (Open, High, etc.), I got weak probability estimates, so I'm overlooking those series at the moment.
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I think we are deviating from the question here, and also I think your notation means something else than my notation.

What I wrote is the price changes, not the price at a give time. Is that what you meant by p(t). If I denote two variable: X(t) the price at time t, and P(t) the price change at t with respect to t-1, then:

X(t)=X(t-1)+P(t). (This is too rough since to be more precise we have to think in terms of returns and not in terms of price changes in linear scale, or equivalently in terms of log scale and not in terms of linear scale).

In one minute X(1) is then the open price, X(390) is the close.
The probability that X(390) is greater or equal to x(1) is 0.5.

But the variance of X(t) will grow linearly with square root of time, assuming the hypothesis of independence.

Why is independence important:
---------------------------------------

It is not to develop a trading system, but to calculate the probability to pick the top of a day, and to understand things more deeply.

So if that prob (which is still to be determined) is tiny, would my performance be an accident or is it due to something else?

That is the question we have to answer first, and the hypothesis that have to be tested (with supporting numbers)

It may seem not important to you to study the question under the hypothesis of indepence, but if you were to study this, then you would be on a path to discover your own profitable methods.

By the way you would realize that you will not need to pick the time which such a precision as I did, but reaching that level will come as a by-product of your laboring on the problem.

Let me first read your reaction to what I wrote.
 
Quote from zerfetzen:

I'd never ram something down other people's throats; to each his own. But I do think this is an appropriate thread to discuss statistics if anyone's interested.
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Do not worry about that comment. He was civil. There are people who behave like in a zoo (check my threads :) ) I had even to insult them in return to show that I can also be an a-hole. This is after the market showed that I am right. That is the reason why I think that someone who is methodical like you, should be able to beat their socks off (that is the reason why buffet makes money, he thinks in statistical terms, even if he uses other words for it).
 
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